Now, when I get my hands on a game where I can create my own character, I create a whole buncha chars, both genders, and end up picking the most interesting ones, based on design and concept. Whenever it's relevant to the gameplay, I pick one to be the "good one" and other to be the "evil one", without any gender-related instance. In TES series, my main character is a male because I'm too used to him. In Fallout 3 and NV, I started with a female character that I enjoyed a lot, created a male that was far more awesome, and ended up creating another male who sums up about everything playing FO is to me. In other games, my character is as much of one gender as of the other, based in how much I enjoyed the results I achieved. It depends on the mood, on what do you think will fit with that particular game experience, and there's no point of having the flexibility of creating a custom character if you let something as pragmatic as your natural physiology make the decisions for you. If you feel you can connect better with a person of your gender, fine. If you find more pleasant to look at something you find attractive, fine as well.
I find particularly interesting how much people atribute sixual desires about these matters. Being a bit of cartoonist myself, and having a strong emphasis on character design, I get asked a lot why do I draw so many females, and why they're generally so sixualized. I simply find it very interesting drawing them, hell yes, I like them sixy, and I surely think I'm entitled to portrait my characters in any way I see fit, but sometimes I'm amazed of how much sixual appeal people find on a drawing I do without even thinking about it at all. Whenever I find it interesting, and it is very often, I draw males, old men and women alike, children and animals, robots, monsters and all kind of nonsense. But people are always commenting on the females. I ended up concluding that the meaning is actually on those person's eyes and minds. I'm just drawing.
Yeah yeah, "yap yap TL/DR".